The present invention relates, in general, to resilient support devices for mounting oscillating bodies on support structures, and is particularly concerned with a damped resilient support device of the type including a tubular support body for fixing to the support structure, an attachment member which is attachable to the oscillating body and is connected coaxially to one end of the tubular support body by an annular elastomeric element the outer surface of which is fixed to the tubular support body and the inner surface of which is fixed to the attachment member, and a fluid-dynamic damper for damping oscillations of the attachment member relative to the tubular support body.